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Journal of Algebra
One of the main purposes of this paper is to give examples of relatively Ž . free semigroups and monoids having intermediate growth Section 6 . ... Quite recently our methods helped us to construct examples of relatively free semigroups of Ž . intermediate growth and maximal equals 1 Gelfand᎐Kirillov superdimension. ... The equality 160 shows that induces a one-to-one correspondence Ä 4 between the set of all finite sequences ␣ as above and the set of all n words of the type ⌬ U over the alphabet ⌽. ...doi:10.1006/jabr.2000.8503 fatcat:5l2omizwljdpvm2qqnf6tokhzy
Mat. 54 (1990), no. 5, 899-927; MR 92h:16020] the author presents the following broad result: if T is the semigroup of automorphisms of a free countably generated algebra over a field of characteristic ... 0, and R is a relatively free algebra satisfying a standard identity, then R is Noetherian as an F-module. ...
Journal of Algebra
Some applications including examples of f.g. relatively free semigroups having intermediate growth and maximal (equals 1) superdimension are considered. 483 Let U be a word over the alphabet Λ and W a ... Furthermore, the length of the period is bounded above by a constant which depends only on the number n and on the number of generators of S. ... We also find the first example of a relatively free f.g. semigroup which has intermediate growth and superdimension 1 (Theorem 4.1) and a similar example of a semigroup which is nilpotent in the sense ...doi:10.1016/j.jalgebra.2003.09.021 fatcat:ggdkpnq4cna3begbds2tc24vdi
But the appropriate formula exists in terms of formal power series. The result is obtained in generality of free Lie superalgebras, graded by some semigroups. ... In this case instead of formal power series we use elements of the completion of a semigroup ring, which are called characters. ... In particular, this is the case, if A is a relatively free superalgebra of some variety with the generating set X = X + ∪ X − . ...doi:10.1016/s0012-365x(01)00262-x fatcat:ewc4vask4nekxjwqg4fzjoj42i
relatively free) algebras. ... A.A.Kirillov and M.L.Koncevich  constructed a relatively free Lie algebra of an intermediate growth: the Lie algebra of generic vector elds on a variety. ... The method of generalization uses the passage to an associative algebra of (left) ...doi:10.1007/bf02355446 fatcat:zt4izxi4yzhd7mx5o7lufa2ika
CRM Proceedings and Lecture notes AMS
For example, the maximal number of independent vector fields on the n-sphere was determined explicitly. ... From these classical descriptions we move via spaces of unbounded operators and super-semigroups of operators to our most recent model, which is given by certain spaces of supersymmetric (1|1)-dimensional ... referred to as the superdimension. ...doi:10.1090/crmp/050/20 fatcat:s3kjzsqnznaupldmukl7y6phym
Concise Encyclopedia of Supersymmetry
Semigroup congruences are important for the study and classification of complex physical phenomena, especially when applied to free semigroups and monoids. Bibliography  A. H. Clifford and G. B. ... T from the set of elements of semigroup S into the set of elements of semigroup T such that /ðxyÞ ¼ /ðxÞ/ðyÞ for all x; y 2 S. When / is bijective, then S and T are isomorphic semigroups. ... A simple example is the following one for a free model of where Q BRS ic a k a ; @t . This is an N ¼ 2 supersymmetry. ...doi:10.1007/1-4020-4522-0_474 fatcat:f42ycwddmjbqva6u6dtues4ig4
We use these results to construct five new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds, contributing to the classification of the V_1-structures of suitably regular, ... To this end we describe the fusion algebra of the fixed-point vertex operator subalgebra V^G and show that V^G has group-like fusion. ... I enjoyed working together with both of them on the paper [EMS15] , which is partly based on this dissertation and vice versa. ...arXiv:1611.09843v2 fatcat:ni2mohubjje67gcix7t5dtfeyq